发表机构
Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在有限结果空间的条件查询假设检验模型中，证明可学习性依赖分布类的成对条件概率正间隔，构建了可匹配自适应策略的非随机构建过程，得出交互仅带来二次方量级的查询效率提升而非指数级优势的结论。
AI 中文摘要
模型评估可以在观测到任何响应前确定所有测试，也可以利用早期响应选择后续测试。我们在结果空间有限（|X|=N）的条件查询模型中研究这一选择。我们首先探究哪些分布类对可以被可靠区分，随后研究当所有查询事件必须预先固定时，需要多少额外查询才能匹配自适应测试器的性能。我们证明，可学习性成立当且仅当两类分布的成对条件概率存在正间隔。当该间隔为零时，在任意有限查询预算下，最优最坏情况误差恰好为1/2。对于任意T次查询的自适应策略和任意ρ∈(0,1)，我们构建了一种随机非自适应过程，使用在观测任何响应前选定的O(N²(T + log(1/ρ)))个成对查询，其模拟转录本与自适应转录本的总变差距离不超过ρ，且对模型中所有分布一致成立。我们还构建了一组匹配的分布类，其自适应查询复杂度为常数，而非自适应查询复杂度为Ω_ε(N²)。因此，最坏情况下的固定误差自适应间隔为Θ_ε(N²)。这表明交互可以将所需测试数量减少二次方量级，但交互式评估表面上的指数分支并不会带来指数级的查询优势。
英文摘要
Model evaluations may fix all tests before observing any responses or select later tests using earlier responses. We study this choice in a conditional-query model on a finite outcome space $\mathcal{X}$ with $|\mathcal{X}|=N$. We first ask which pairs of distribution classes can be reliably distinguished. We then ask how many additional queries are required to match an adaptive tester when all queried events must be fixed in advance. We show that learnability holds if and only if the two classes have positive separation in their pairwise conditional probabilities. When this separation is zero, the optimal worst-case error is exactly $1/2$ at every finite query budget. For any $T$-query adaptive policy and any $ρ\in (0,1)$, we construct a randomized non-adaptive procedure using $O(N^2(T + \log(1/ρ)))$ pair queries chosen before any response is observed. Its simulated transcript is within $ρ$ in total variation of the adaptive transcript, uniformly over all distributions in the model. We also construct a matching family with constant adaptive query complexity and $Ω_\varepsilon(N^2)$ non-adaptive query complexity. Consequently, the worst-case fixed-error adaptivity gap is $Θ_\varepsilon(N^2)$. Thus interaction can reduce the required number of tests by a quadratic factor, but the apparent exponential branching of an interactive evaluation does not yield an exponential query advantage.
Comments18 pages
